Super Lie algebra play also an important role in supersymmetric theories since they precisely encode the supersymmetry of a given physical model. Among the most interesting superalgebras are the extensions of the (trivial) Lie algebra of translations of the Minkowski space-time (this is then the super Lie algebra of super translations of space-time) or of the Poincaré Lie algebra (called the super Poincaré Lie algebra). We present examples of such Lie super algebras in Section . Lie super algebras are naturally associated with Lie super groups, which are particular examples of supermanifolds. However a Lie super algebra as defined here is a skeletal object, which needs some extra `flesh' for the construction of the corresponding Lie group (what we would call a Lie algebra with flesh corresponds actually to a super Lie module, see [1]}).
